Multi-scale dynamics and non-smooth modal analysis of damageable engineering structures

Mostafa Attar Khorassani

    Research output: ThesisDoctoral Thesis

    361 Downloads (Pure)


    The structural dynamics of mechanical components can be highly influenced bythe presence of imperfections. For practical purposes, the development of novelnumerical tools to address the adverse influences of defects on the dynamics ofmechanical systems is of the highest interest for today’s engineering applications.

    This PhD thesis aims to investigate the application of the discrete lattice methodfor dynamic analysis of engineering structures subjected to defects. The discretelattice method is a multi-scale modelling tool (micro-to-macro technique) which isused to represent the matter as a network of discrete units (particles) while they areinteracting through the connecting elements. Therefore, the interactions betweenthe particles at small scale reproduce the mechanical behaviour of the system atlarge scale. Two scenarios for the damages are considered in this thesis. Firstly,the dynamic behaviour of the structural components weakened by local defects isstudied. These local damages are interpreted as surface cracks that locally induceadditional flexibilities to the linking elements in the discrete model. Subsequently,the non-linear dynamics of the system is investigated when it is subjected todamaged contact constraints. The second type of damage is characterised at thediscrete level by the non-smooth behaviour of restoring forces in contact elements.

    Numerical frameworks and corresponding computer codes are developed topredict the free and forced vibratory responses of such systems. The proposednumerical methods are also verified by comparing to semi-analytical solutionsof simplified problems (when an analytical solution is available) to ensure theefficiency and robustness of the proposed approaches.

    The current thesis is presented in the form of research papers that are alreadypublished or under review for publication in the scholarly international journals.The problems addressed herein include: (i) Structural dynamics of damagedcomponents based on the modal expansion technique: the proposed semi-analyticalsolution provides a reference framework for verification of the proposed numericalmethods. (ii) Free and forced vibration analysis of damaged structures based on anovel discrete lattice method: the adverse effects of local damages are modelledas additional local compliance at discrete level affecting the overall structuralresponse. (iii) Non-smooth dynamics of structural elements once they are subjectedto unilateral constraints: a novel non-smooth modal analysis is performed andsalient features of non-linear normal modes are studied by applying the proposedtime integration scheme in combination with the shooting method.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2015


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